Related papers: A State Polytope Decomposition Formula

It is well known that every non-degenerate quadratic form admits a decomposition into an orthogonal sum of its anisotropic part and a hyperbolic form. This decomposition is unique up to isometry. In this paper we present an algorithm for…

We propose an interpretation of quantum separability based on a physical principle: local time reversal. It immediately leads to a simple characterization of separable quantum states that reproduces results known to hold for binary…

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…

Simultaneous decompositions of a pair of states into pure ones are examined. There are privileged decompositions which are distinguished from all the other ones.

A recently proposed convolution technique for the calculation of local density of states is described more thouroughly and new results of its application are presented. For separable systems the exposed method allows to construct the ldos…

We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present methods to compute the…

We prove a decomposition theorem for orthocomplemented state property systems. More specifically we prove that an orthocomplemented state property system is isomorphic to the direct union of the non classical components of this state…

Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case…

We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this…

We give a formula for matrix exponentials and partial fraction decompositions.

An important measure of bipartite entanglement is the entanglement of formation, which is defined as the minimum average pure state entanglement of all decompositions realizing a given state. A decomposition which achieves this minimum is…

Multipartite entanglement is a natural generalization of bipartite entanglement, but is relatively poorly understood. In this paper, we develop tools to calculate a class of multipartite entanglement measures - known as multi-invariants -…

We derive an integral convex combination of product states for a range of separable Werner states. Our method consists of expanding the sought-after local density operators in terms of Wigner operators. For dimension d=2, our decomposition…

We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the…

We present a new method of analytically deriving the entanglement of formation of the bipartite mixed state. The method realizes the optimal decomposition families of states. Our method can lead to many new results concerning entanglement…

We derive criteria for $k$-separability of multipartite Quantum state

Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szanto. In this paper, we give the first complete bounds for the…

For systems of polynomial equations, we study the problem of computing the Newton polytope of their eliminants. As was shown by Esterov and Khovanskii, such Newton polytopes are mixed fiber polytopes of the Newton polytopes of the input…

We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)].…

We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…